The prophecy was given in the days of Ahaz the king, the father of Hezekiah

Isaiah 7- 1And it came to pass in the days of Ahaz the son of Jotham, the son of Uzziah, king of Judah, that Rezin the king of Syria, and Pekah the son of Remaliah, king of Israel, went up toward Jerusalem to war against it, but could not prevail against it

Ahaz was 20 years old when he became king.

2 kings 16-1 1In the seventeenth year of Pekah the son of Remaliah Ahaz the son of Jotham king of Judah began to reign.2Twenty years old was Ahaz when he began to reign, and reigned sixteen years in Jerusalem, and did not that which was right in the sight of the LORD his God, like David his father.

2 Chronicles 28-1 Ahaz was twenty years old when he began to reign, and he reigned sixteen years in Jerusalem: but he did not that which was right in the sight of the LORD, like David his father:

Ahaz reigned for 16 years, which means he was 36 years old when he died.

Hezekiah was 25 years old when he began to reign.

2 Kings 18-1 Now it came to pass in the third year of Hoshea son of Elah king of Israel, that Hezekiah the son of Ahaz king of Judah began to reign. 2 Twenty and five years old was he when he began to reign; and he reigned twenty and nine years in Jerusalem. His mother’s name also was Abi, the daughter of Zachariah.

This means that Ahaz had to have been around 11/12 years old when Hezekiah was born. This was around 8 years BEFORE he became king. It is therefore IMPOSSIBLE that Hezekiah was yet to be born when Isaiah gave his prophe